A new analytical method for computing concentration-dependent interdiffusion coefficients, when a non-uniform solute distribution pre-exists in a substrate prior to diffusion in a binary system, is developed from Fick’s laws of diffusion. The key concept of the new method is validated by experimental data reported in the literature. This new method addresses the limitations of previous analytical techniques such as Boltzmann–Matano, Saucer–Friese, and Sarafianos methods, which are restricted to a single solute concentration profile, with no non-uniform initial solute distribution. The analyses of numerically simulated concentration profiles show that previous standard analytical methods are erroneous when computing the interdiffusion coefficients in binary systems with significant non-uniform initial solute distributions. In contrast, the new analytical method can reliably compute the concentration-dependent interdiffusion coefficient operative between two isothermal concentration profiles obtained at different diffusion times. Practically, this method can be used to extract concentration-dependent interdiffusion coefficients from planar diffusion systems with non-uniform initial solute distribution caused by pre-diffusion or multi-staged diffusion processes.

根据扩散的菲克定律，开发了一种新的分析方法，用于计算浓度相关的互扩散系数，当在二元体系中扩散之前在基板中预先存在不均匀的溶质分布时。通过文献报道的实验数据验证了该新方法的关键概念。这种新方法解决了以前的分析技术的局限性，例如Boltzmann–Matano，Saucer–Friese和Sarafianos方法，这些方法仅限于单个溶质浓度曲线，并且没有非均匀的初始溶质分布。数值模拟浓度分布图的分析表明，当在具有显着不均匀初始溶质分布的二元系统中计算互扩散系数时，先前的标准分析方法是错误的。相比之下，新的分析方法可以可靠地计算在不同扩散时间获得的两个等温浓度曲线之间可操作的浓度相关的互扩散系数。实际上，该方法可用于从平面扩散系统中提取浓度相关的互扩散系数，该平面扩散系统具有由预扩散或多阶段扩散过程引起的初始溶质分布不均匀的现象。